Are the technical details of Filmic available?
Blender is a package of view transforms created to convert Scene-Referred image data into Display-Referred values, using a large dynamic range and de-saturating the highlights so that they resemble images created on a film camera.  

Refer to: Render with a wider dynamic range in cycles to produce photorealistic looking images

Blender's Color management is implemented through OpenColorIO (https://opencolorio.org/). That might be the place to start a journey that will take you down the rabbit hole of color.

The file with the rules used for color managenment can be found in 
/blender/(blender version)/datafiles/colormanagement/config.ocio.

The definitions and stanzas on such config.ocio file are written to be interpreted by OCIO and determine how data is transformed, and if LUTs are used.

LUTs used for transformations are contained in the luts and views sub-folders within the color management folder.

How to make 3D LUTs and use them in Blender?

To use filmic, you would need an app that is OCIO aware. (Nuke, Mari, AffinityPhoto, Krita and others already use it, so there might be no need to re-invent the wheel).

Image data must first be converted to use Rec709/sRGB primaries, transformed to linear values, and then scaled to be real scene-referred data (or at least to fall within the range used by filmic).

If the image is generated on a camera, the de-saturation and conversion to display referred might have already taken place, so there might be nothing to be gained by using filmic, even when shooting raw. Filmic was intended for CG rendered imagery. It was meant to overcome the limitations of using sRGB transforms and to solve the non-existing cross-talk between color channels during rendering. Camera sensors and filters work in a completely different way to create images. The filters over the sensor, that define color, allow for some overlap of different frequencies, making the color saturation at the bright parts of the image more "film like".

Other kinds of transformations might be more useful than "filmic" for in-camera generated images .